# T-test vs F-test vs Z-test | Difference between T-test, F-test, Z-test

This page compares T-test vs F-test vs Z-test and mentions **difference between** T-test, F-test and Z-test.
The applications of T-test, F-test and Z-test are also mentioned.

**What is hypothesis**:

• It is a predictive statement capable of being tested by scientific methods.

• Hypothesis is simple proposition which can be proved or disproved through
various scientific techniques.

• It establishes relationship between independent variable to some dependent variable.

• All these three are hypothesis tests.

• Entire decision to validate or to refuse the null hypothesis is based on
these tests. Hence it is essential to choose the right test.

## T-test

• It is a univariate hypothesis test.

• It is applied in condition when standard deviation is not known and
sample size is small (n < 30).

• It is used to compare means of two populations.

• T-test is commonly used compare to z-test as explained below.

• Test statistic and assumption for T-test is mentioned for one sample test.
Similarly two sample t-test, paired t-test are performed for
various applications.

## F-test

• It is a statistical test.

• It is used to determine equality of variances of two normal populations.

• It is used to compare two population variances.

• This test is based on snedecor f-distribution (under null hypothesis).

• Test statistic for F-test is mentioned. It is known as one-way ANOVA test.
It is used to test difference of three or more population means.

## Z-test

• It is also statistical hypothesis test which follows normal
distribution.

• It is applied to moderate to large samples (i.e. when n > 30).

• It is used to determine whether two population means are different when
variances are known and sample size is large as mentioned.

• Z-test depends on certain conditions in order to be reliable.
Hence it is less adaptable compare to T-test.

• Z-test is preferable compare to T-test when standard deviation values are available or
known.

• Test statistic and assumption for Z-test is mentioned for one sample test.

Following table summarizes difference between these parametric test types.

Features |
F-test |
T-test |
Z-test |
---|---|---|---|

Application | Comparing variances of two samples | Comparing the mean to a value, or the means of two samples | same as T-test but for large samples |

Used when | 3 or more μ_{s} |
n < 30 and σ is unknown | n >= 30 and σ is known |

## What is difference between or comparison between

Following links mention difference or comparison between various equipments and terms:

comparison between SPI and I2C

difference between PXI and PCI

Microscope vs Telescope

Amplitude Modulation vs Angle Modulation

difference between modem and router

Air Fuel Ratio Sensor vs O2 Sensor

Radiometer vs Spectrometer vs Spectroradiometer

Clamp meter vs digital multimeter

Colorimeter vs Spectrophotometer

difference between Prism and Grating

difference between Venturi meter and Orifice meter

difference between Lux and Lumens